DOI: 10.1111/musa.12133 TREVOR RAWBONE AND STEVEN JAN THE BUTTERFLY SCHEMA IN THE CLASSICAL INSTRUMENTAL STYLE:A PRODUCT OF THE TENDENCY FOR CONGRUENCE Synthesising Associative-Statistical and Generative Theories of Schemata through the Notion of Congruence In the fields of music theory and music cognition, localised multiparametric schemata receive various explications and definitions. While these cannot be precisely pigeonholed, they do favour classification in terms of a loosely associative-statistical or generative orientation. From an associative-statistical standpoint, schemata form in cognition through the mental association of statistically predominant features in time and place, such as the conglomerations of voice-leading patterns, figured progressions and metrical structures in Leonard B. Meyer (1973), Robert O. Gjerdingen (1988, 1996 and 2007) and Vasili Byros (2009). For example, the 1–7 . . . 4–3 voice-leading schema appears to rise and fall in history in a cycle of popularity and typicality resembling a bell curve, peaking in the early 1770s, ‘due to the way brains abstract stable categories from a continuum of historical change’ (Gjerdingen 1988, p. 99). Thus, in this view, schemata are a form of culturally situated cognition (Gjerdingen 2007 and Byros 2012). By contrast, in the generative paradigm, schemata emerge as stable descriptions of the tonal grammar, generated by a system of well-formedness and preference rules that are a product of universal cognitive capacities (Lerdahl and Jackendoff 1983, Lerdahl 2001 and Temperley 2001), such as Fred Lerdahl’s and Ray Jackendoff’s ‘normative structure’ (1983, p. 289). Broadly, schemata are particular structures in associative-statistical theories, and general or universal structures in generative theories. In terms of underlying metaphysical foundations, the associative-statistical programme is loosely underpinned by empiricist theories of knowledge, following the British empiricist philosophers, including John Locke (1632– 1704), George Berkeley (1685–1753) and David Hume (1711–1776), who were concerned with the influence of the environment or culture on behaviour. However, the generative paradigm embraces rationalist philosophy stemming from the ‘continental rationalism’ of Ren´ e Descartes (1596–1650), Baruch Spinoza (1632–1677) and Gottfried Leibniz (1646–1716), which involves the representational, combinatorial and computational structure of internal cognitive capacities. Notwithstanding these philosophical distinctions, both associative-statistical and generative models incorporate primary chords, regular harmonic rhythms, Music Analysis, 00/0 (2019) 1 © 2019 The Authors. Music Analysis © 2019 John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA